Question

How do you solve `\frac { \frac { 6} { y } } { \frac { 9} { y - 6} }`?

Answer 1

See the entire solution process below:

Explanation:

First, use this rule for dividing fractions:

`(color(red)(a)/color(blue)(b))/(color(green)(c)/color(purple)(d)) = (color(red)(a) xx color(purple)(d))/(color(blue)(b) xx color(green)(c))`

`(color(red)(6)/color(blue)(y))/(color(green)(9)/color(purple)(y - 6)) = (color(red)(6) xx color(purple)((y - 6)))/(color(blue)(y) xx color(green)(9)) = (color(red)((3 xx 2)) xx color(purple)((y - 6)))/(color(blue)(y) xx color(green)((3 xx 3))) =`

`(color(red)((cancel(3) xx 2)) xx color(purple)((y - 6)))/(color(blue)(y) xx color(green)((cancel(3) xx 3))) = (color(red)(2) xx color(purple)((y - 6)))/(color(blue)(y) xx color(green)(3)) = ((color(red)(2) xx color(purple)(y)) - (color(red)(2) xx color(purple)(6)))/(3y) =`

`(2y - 12)/(3y)`

Or:

`(2y - 12)/(3y) = (2y)/(3y) - 12/(3y) = (2y)/(3y) - (3 xx 4)/(3y) =`

`(2color(red)(cancel(color(black)(y))))/(3color(red)(cancel(color(black)(y)))) - (color(blue)(cancel(color(black)(3))) xx 4)/(color(blue)(cancel(color(black)(3)))y) = 2/3 - 4/y`